Formulas

Elementary Algebra

Proportions

A proportion is the equality of two ratios:
\({\large\frac{a}{b}\normalsize} = {\large\frac{c}{d}\normalsize}\)
The terms \(a\) and \(d\) are called the extremes and \(b\) and \(c\) are called the means.

Means-Extremes (Cross-Products) property
The product of the means \(b\) and \(c\) is equal to the product of the extremes \(a\) and \(d:\)\({\large\frac{a}{b}\normalsize} = {\large\frac{c}{d}\normalsize}\;\) \(\Rightarrow \;ad = bc\)

Rule of Three
The Rule of Three is used to find the \(4\)th term in a proportion when the other \(3\) terms are known:
If \({\large\frac{a}{b}\normalsize} = {\large\frac{c}{x}\normalsize},\) then \(x = {\large\frac{bc}{a}\normalsize}.\)